Ultrasonic transducers are used in a variety of applications to create high frequency vibration of a vibrating element. The vibrating element may in turn be used to atomize a liquid, clean delicate objects such as jewelry, cut and coagulate tissue during surgical procedures, disrupt tissues in the process of sample preparation in a microbiological lab, or to perform another operation. For the purposes of this disclosure, an ultrasonic transducer is a device that is supplied with an oscillating electrical signal, such as a voltage, and causes an ultrasonic mechanical oscillation of a vibrating element. The mechanical vibration typically occurs fundamentally at the same frequency as the frequency of the applied oscillating electrical signal. An ultrasonic transducer may include, for example, a piezoelectric element that changes its geometry in response to changes in applied voltage. In some applications, the mechanically vibrating element may be called an end effector, and may be a probe, blade, or other device. Depending on the application, an end effector may freely vibrate in air or liquid, or may come in contact with tissue or other objects. The transducer and end effector may have a resonant frequency at which the amplitude of vibration of the end effector is maximized.